Finite Group Databasebeta

← #10846060

Subgroups — #10846060

Order 768.

1184 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2535C211yesmaximal, characteristic, complemented
2C2×#5039C211yesmaximal, characteristic, complemented
3C2×#5038C211yesmaximal, characteristic, complemented
4#82378C211yesmaximal, characteristic, complemented
5C2×#5015C211yesmaximal, characteristic, complemented
6C2×#5011C211yesmaximal, characteristic, complemented
7#71684C211yesmaximal, characteristic, complemented
8#71684C211yesmaximal, characteristic, complemented
9#71609C211yesmaximal, characteristic, complemented
10#69553C211yesmaximal, characteristic, complemented
11#69540C211yesmaximal, characteristic, complemented
12#69524C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic, complemented
14#69517C211yesmaximal, characteristic, complemented
15#69515C211yesmaximal, characteristic, complemented
16#25396—31nomaximal, Sylow
17C2×C3×#121C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#940—21no—
22C22×#213C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C2×#930C2211yescharacteristic
25C2×#930C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C22×#208C2211yescharacteristic
29C23×C3⋊C8C2211yescharacteristic
30C2×#874C2211yescharacteristic
31C3×#397—21no—
32C3×#392—21no—
33C3×#386—21no—
34C3×#386—21no—
35C3×#382C2211yescharacteristic
36C3×#380C2211yescharacteristic
37C3×#380C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42#5039—24no—
43#5038—24no—
44#5015—24no—
45#5011—24no—
46#4988—21no—
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#808C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4960—21no—
56#4960—21no—
57C4×C4⋊Dic3C2211yescharacteristic
58C2×C4⋊(C3⋊C8)C2211yescharacteristic
59C2×#803C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#469—31no—
65C2×#466—31no—
66C2×#459—31no—
67C2×#435—31no—
68#2541—31no—
69#2535D311yescharacteristic, complemented
70#2034—31no—
71#2033—31no—
72#1999—31no—
73#1999—31no—
74#1961—31no—
75#1949—31no—
76#1895—31no—
77#1893—31no—
78#1762—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4D411yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C22×#67—21no—
88C22×#67—21no—
89C22×#67—21no—
90C22×D12—21no—
91C22×D12—21no—
92C22×D12C2311yescharacteristic
93C22×D12C2311yescharacteristic
94C3×#121—22no—
95C3×#121—22no—
96C3×#121—41no—
97C3×#121—41no—
98C3×C4×D4—22no—
99C3×C4×D4—22no—
100C3×C4×D4—22no—
101C3×C4×D4—22no—
102C2×C3×C4⋊C4D411yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4D411yescharacteristic
112C2×C3×C22⋊C4D411yescharacteristic
113C2×C3×C42C2311yescharacteristic
114#940—44no—
115C2×#213—22no—
116C2×#213—22no—
117C2×#213—22no—
118C2×#213—22no—
119C2×#213—41no—
120C2×#213—41no—
121#930—22no—
122#930—22no—
123#930—22no—
124#930—22no—
125#930—41no—
126#930—41no—
127#930—41no—
128#930—41no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4×Dic3—21no—
136C2×#208—22no—
137C2×#208—22no—
138C2×#208—41no—
139C22×C3⋊C8—22no—
140C22×C3⋊C8—22no—
141C22×C3⋊C8—41no—
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146#874—22no—
147#874—22no—
148C3×#95—21no—
149C3×#95—21no—
150C3×#95—21no—
151C3×#95—21no—
152#832—22no—
153#832D414yescomplemented
154C3⋊#95—21no—
155#830—22no—
156#830—22no—
157#809—22no—
158#809—22no—
159#809—22no—
160#809—22no—
161#809—41no—
162#809—41no—
163#808—22no—
164#807—22no—
165C4⋊(C3⋊C8)D414yescomplemented
166#803—22no—
167C22×D8—31no—
168C22×D8—31no—
169C22×M16—31no—
170C23×C8—31no—
171C2×#127—31no—
172C2×#127—61no—
173C2×#121—31no—
174C2×#121—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×#121C2×D311yescharacteristic
178C2×#121C2×D311yescharacteristic
179C2×C4×D4C2×D311yescharacteristic
180C2×C4×D4C2×D311yescharacteristic
181#469—64no—
182#466—64no—
183#459—64no—
184#435—64no—
185C2×#107—31no—
186C2×#106—31no—
187C2×C4⋊C8—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×#97—31no—
199#397—21no—
200#392—21no—
201#392—61no—
202#392—61no—
203#390—61no—
204#386—21no—
205#386—21no—
206#382C2×D311yescharacteristic
207#380C2×D311yescharacteristic
208#380C2×D311yescharacteristic
209C4×C4⋊C4—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214C24×C3—21no—
215C24×C3C2×D411yescharacteristic
216C24×C3C2×D411yescharacteristic
217C23×D3—21no—
218C23×D3—21no—
219C2×C3×D4—22no—
220C2×C3×D4—22no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—41no—
227C2×C3×D4—42no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—81no—
232C2×C3×D4—81no—
233C2×C3×D4C2×D412yes—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—42no—
250C22×C3×C4—81no—
251C22×C3×C4—81no—
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2411yescharacteristic
257C2×#67—42no—
258C2×#67—42no—
259C2×#67—42no—
260C2×#67—42no—
261C2×#67—42no—
262C2×#67—42no—
263C2×#67—42no—
264C2×#67—42no—
265C2×#67—81no—
266C2×#67—81no—
267C2×#67—81no—
268C2×#67—81no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—42no—
284C2×D12—42no—
285C2×D12—42no—
286C2×D12—42no—
287C2×D12—81no—
288C2×D12—81no—
289C3×C4⋊C4—22no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C22⋊C4—22no—
297C3×C22⋊C4—22no—
298C3×C22⋊C4—42no—
299C3×C22⋊C4—42no—
300C3×C22⋊C4—42no—
301C3×C22⋊C4—81no—
302C3×C22⋊C4—81no—
303C3×C42C2×D412yes—
304C3×C42#4112yes—
305#213—44no—
306#213—44no—
307(C2×D3)⋊C4—42no—
308(C2×D3)⋊C4—42no—
309(C2×D3)⋊C4—42no—
310(C2×D3)⋊C4—42no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3C2×D412yes—
314C4⋊Dic3#4112yes—
315C4×Dic3—42no—
316#208—44no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—44no—
327C2×C3⋊C8C2×D412yes—
328C2×C3⋊C8C2×D412yes—
329C2×C3⋊C8C2×D412yes—
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—31no—
333C22×D4—31no—
334C22×D4—61no—
335C22×D4—61no—
336C22×D4—61no—
337C22×D4—61no—
338C22×D4—61no—
339C22×D4—61no—
340C22×D4#6711yescharacteristic
341C22×D4C22×D311yescharacteristic
342C23×C4—21no—
343C23×C4C22×D311yescharacteristic
344C23×C4C22×D311yescharacteristic
345C2×D8—62no—
346C2×D8—62no—
347C2×D8—62no—
348C2×D8—62no—
349C2×D8—121no—
350C2×D8—121no—
351C2×M16—62no—
352C2×M16—62no—
353C2×M16—121no—
354C22×C8—31no—
355C22×C8—31no—
356C22×C8—31no—
357C22×C8—31no—
358C22×C8—62no—
359C22×C8—62no—
360C22×C8—121no—
361#127—62no—
362#127—62no—
363#127—124no—
364#121—22no—
365#121—22no—
366#121—41no—
367#121—41no—
368#121—62no—
369#121—62no—
370#121—62no—
371#121—62no—
372#121—121no—
373#121—121no—
374#121—121no—
375#121—121no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4#6711yescharacteristic
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C4⋊C4C22×D311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4#6711yescharacteristic
396C2×C22⋊C4#6711yescharacteristic
397C2×C42—61no—
398C2×C42C22×D311yescharacteristic
399#107—62no—
400#106—62no—
401C4⋊C8—34no—
402#102—34no—
403#102—62no—
404#102—62no—
405#102—62no—
406#102—62no—
407#102—62no—
408#102—121no—
409#102—121no—
410C22⋊C8—62no—
411C22⋊C8—62no—
412#97—62no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—61no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—22no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3AGL(1,ℤ/8)12yes—
439C23×C3C22×D411yescharacteristic
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C3×D4—22no—
455C3×D4—22no—
456C3×D4—44no—
457C3×D4—41no—
458C3×D4—41no—
459C3×D4—84no—
460C3×D4—84no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—84no—
489C2×C3×C4#12112yes—
490C2×C3×C4#12112yes—
491C2×C3×C4C22×D411yescharacteristic
492C2×C3×C4C22×D411yescharacteristic
493C2×C3×C4C2×#4111yescharacteristic
494C2×C3×C4C2×#4111yescharacteristic
495C2×C3×C4H(5,𝔽2)11yescharacteristic
496C2×C3×C4H(5,𝔽2)11yescharacteristic
497#67—84no—
498#67—84no—
499#67—84no—
500#67—84no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507D12—41no—
508D12—41no—
509D12—41no—
510D12—41no—
511D12—41no—
512D12—41no—
513D12—41no—
514D12—41no—
515D12—84no—
516D12—84no—
517C3⋊C8—22no—
518C3⋊C8—22no—
519C3⋊C8—22no—
520C3⋊C8—41no—
521C24—21no—
522C24—61no—
523C24—61no—
524C24C2×#6711yescharacteristic
525C24C2×#6711yescharacteristic
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—41no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—61no—
539C2×D4—61no—
540C2×D4—61no—
541C2×D4—61no—
542C2×D4—61no—
543C2×D4—61no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—81no—
551C2×D4—81no—
552C2×D4—122no—
553C2×D4—122no—
554C2×D4—122no—
555C2×D4—122no—
556C2×D4—122no—
557C2×D4—122no—
558C2×D4—122no—
559C2×D4—122no—
560C2×D4—122no—
561C2×D4—122no—
562C2×D4—122no—
563C2×D4—122no—
564C2×D4—241no—
565C2×D4—241no—
566C2×D4—241no—
567C2×D4—241no—
568C2×D4—241no—
569C2×D4—241no—
570C2×D4D3×D412yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—42no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4C2×#6711yescharacteristic
592C22×C4C2×#6711yescharacteristic
593C22×C4C2×#6711yescharacteristic
594C22×C4C2×#6711yescharacteristic
595C22×C4C23×D311yescharacteristic
596D8—124no—
597D8—124no—
598M16—124no—
599C2×C8—32no—
600C2×C8—32no—
601C2×C8—32no—
602C2×C8—61no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—61no—
609C2×C8—61no—
610C2×C8—61no—
611C2×C8—124no—
612C4⋊C4—22no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—32no—
620C4⋊C4—32no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—122no—
631C22⋊C4—122no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C42—122no—
635C42D3×D412yes—
636C42#23712yes—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—42no—
646C22×C3—41no—
647C22×C3—42no—
648C22×C3—41no—
649C22×C3—42no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3C2×#12111yescharacteristic
659C22×C3D4211yescharacteristic
660C22×C3#54611yescharacteristic
661C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
662C22×C3#57511yescharacteristic
663C22×C3#57611yescharacteristic
664C22×C3#57611yescharacteristic
665C2×D3—81no—
666C2×D3—81no—
667C2×D3—81no—
668C2×D3—81no—
669C2×D3—81no—
670C2×D3—81no—
671C2×D3—81no—
672C2×D3—81no—
673C2×D3—81no—
674C2×D3—81no—
675C2×D3—81no—
676C2×D3—81no—
677C2×D3—81no—
678C2×D3—81no—
679C3×C4—22no—
680C3×C4—22no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—81no—
684C3×C4—81no—
685C3×C4—81no—
686C3×C4#53211yescharacteristic
687C3×C4#54011yescharacteristic
688C3×C4D4211yescharacteristic
689C3×C4#55011yescharacteristic
690Dic3—42no—
691Dic3—42no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—121no—
713C23—121no—
714C23—121no—
715C23—121no—
716C23—121no—
717C23—121no—
718C23—121no—
719C23—121no—
720C23—121no—
721C23—121no—
722C23—121no—
723C23—121no—
724C23—121no—
725C23—121no—
726C23#94912yes—
727C23C22×#6711yescharacteristic
728D4—22no—
729D4—22no—
730D4—44no—
731D4—41no—
732D4—41no—
733D4—84no—
734D4—84no—
735D4—121no—
736D4—121no—
737D4—121no—
738D4—121no—
739D4—121no—
740D4—121no—
741D4—121no—
742D4—121no—
743D4—244no—
744D4—244no—
745D4—244no—
746D4—244no—
747D4—244no—
748D4—244no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—84no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4#93912yes—
784C2×C4#93912yes—
785C2×C4C2×D3×D411yescharacteristic
786C2×C4C2×D3×D411yescharacteristic
787C2×C4C2×#23711yescharacteristic
788C2×C4#100411yescharacteristic
789C2×C4D3×#4111yescharacteristic
790C2×C4#100911yescharacteristic
791C8—62no—
792C8—62no—
793C8—62no—
794C8—121no—
795C2×C3—42no—
796C2×C3—81no—
797C2×C3—82no—
798C2×C3#242811yescharacteristic
799C2×C3#305511yescharacteristic
800C2×C3#305811yescharacteristic
801C2×C3#326411yescharacteristic
802C2×C3#326811yescharacteristic
803C2×C3#330911yescharacteristic
804C2×C3#331811yescharacteristic
805D3—161no—
806D3—161no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—41no—
816C22—41no—
817C22—42no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—42no—
823C22—41no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—241no—
829C22—241no—
830C22—241no—
831C22—241no—
832C22—241no—
833C22—241no—
834C22—241no—
835C22—241no—
836C22—241no—
837C22—241no—
838C22—241no—
839C22—241no—
840C22—241no—
841C22—241no—
842C22D4×#6711yescharacteristic
843C22C2×#93911yescharacteristic
844C22C2×#94911yescharacteristic
845C22#582211yescharacteristic
846C22#582911yescharacteristic
847C22#583511yescharacteristic
848C22#583511yescharacteristic
849C4—22no—
850C4—22no—
851C4—41no—
852C4—41no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4—122no—
857C4—122no—
858C4#559611yescharacteristic
859C4#559911yescharacteristic
860C4#560911yescharacteristic
861C4#561911yescharacteristic
862C3#2539611yescharacteristic, complemented, Sylow
863C2—42no—
864C2—81no—
865C2—82no—
866C2—481no—
867C2—481no—
868C2#8264911yescharacteristic
869C2#8292411yescharacteristic
870C2#8337811yescharacteristic
871C2#8350211yescharacteristic
872C2#8350711yescharacteristic
873C2#8361611yescharacteristic
874C2#8361911yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2535C2
socleC23×C3C22×D4
hypercenter#2535D3
hypocenterC3#25396
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#2535C2semidirect
2. C2×#5039C2semidirect
3. C2×#5038C2semidirect
4. #82378C2semidirect
5. C2×#5015C2semidirect
6. C2×#5011C2semidirect
7. #71684C2semidirect
8. #71684C2semidirect
9. #71609C2semidirect
10. #69553C2semidirect
11. #69540C2semidirect
12. #69524C2semidirect
13. #69523C2semidirect
14. #69517C2semidirect
15. #69515C2semidirect
69. #2535D3semidirect
153. #832D4semidirect
165. C4⋊(C3⋊C8)D4semidirect
862. C3#25396semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#25352
C2×#50392
C2×#50382
#823782
C2×#50152
C2×#50112
#716842
#716092
#695532
#695402
#695242
#695232
#695172
#695152
#253963